We presented two variants of Bregman Condat–Vũ algorithms,
introduced a line search technique
for the Bregman dual Condat–Vũ algorithm for equality-constrained
problems, and proposed a Bregman extension to PD3O.
Many open questions remain.
It is unclear how to use Bregman distances in PDDY,
and how to extend the line search technique to Bregman PD3O,
the Bregman primal Condat–Vũ algorithm,
and the more general problem (REF ).
Moreover, in the current backtracking technique the ratio of the
primal and dual stepsizes is fixed.
A further improvement would be to relax this constraint
[1]}, [2]}.
